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edge detector and points along the nasal boundary with high curvature (“critical” points) and
negative curvature values are detected. Then, the two alare points are selected as the outer
left and outer right critical points.
For the remaining points (inner and outer eyes and outer mouth) a solution based on the SIFT
detector applied to local search windows is applied. In particular, the extraction of these
points proceeds in cascade using the location of the nose tip and the alare points to identify
a set of the search windows on the face. In the
en-en
,
ex-ex
and
ch-ch
search windows the
SIFT
detector
algorithm is ran. In fact, SIFT has been defined on 2D grayscale images and
includes a
keypoints detector
and a
feature extractor
(Lowe, 2004). By definition, keypoints
detected by SIFT are mainly located at corner points of an image, so that they can be useful
to capture significant anthropometric face points. The SIFT point detected at the
highest
scale
is retained as the keypoint of the search window. Experiments on the accuracy of the
keypoints detection using this approach can be found in Berretti et al. (2011a).
•
Face Representation with Selected SIFT Features at Facial Keypoints
The nine keypoints automatically detected are used as reference to derive a set of sampling
points of the face. This is obtained by considering 8 lines that connect pairs of keypoints, as
showninFigure5.17
a
. In particular, these lines connect the
nose tip
to the lower point of
the face (
line 1
), the
outer mouth
with the
outer eyes
(
lines 2, 3
), the
inner eyes
with the mid
points of lines 2 and 3 (
lines 4, 5
), the
outer mouth
points each other (
line 6
), and the
alare
points with the
outer mouth
(
lines 7, 8
). Lines are sampled uniformly with a different number
of points as reported in the table of Figure 5.17
b
. According to this, the face is sampled with
a total number of 79 keypoints.
To capture salient features that characterize different facial expressions in 3D, local descrip-
tors are computed around the 79 sample points of the face. The SIFT
feature extraction
algorithm has been used for this purpose to derive SIFT
descriptors
. By computing the
128-dimensional SIFT descriptor at each of the 79 keypoints, a feature vector with 10,112
components is obtained to represent each depth image.
line
#points
indices
1
12
1-12
13-28
29-44
45-53
54-62
63-71
72-75
76-79
2
16
3
16
4
9
5
9
6
9
7
4
8
4
(a)
(b)
Figure 5.17
(a) The eight lines along which the sample points are located (the cropped region of the
face is also reported); (b) the number of points and their indices grouped according to the surface line
they belong to. Copyright
C
2011, Springer
